Journal of Signal and Information Processing, 2011, 2, 266-269

doi:10.4236/jsip.2011.24037 Published Online November 2011 (http://www.SciRP.org/journal/jsip)

Copyright © 2011 SciRes. JSIP

1

Fast Algorithm for DOA Estimation with Partial

Covariance Matrix and without

Eigendecomposition

Jianfeng Chen1, Yuntao Wu2*, Hui Cao2, Hai Wang2

1The 54th Institute of China Electronics Technology Group Corporation, Shijiazhuang, China; 2Key Laboratory of Intelligent Robot

in Hubei Province, Wuhan Institute of Technology, Wuhan, China.

Email: *ytwu@sina.com

Received July 17th, 2011; revised September 10th, 2011; accepted September 18th, 2011.

ABSTRACT

A fast algorithm for DOA estim ation without eigend ecomposition is proposed. Unlike th e availab le propagation method

(PM), the proposed method need only use partial cross-correlation of array output data, and hence the computational

complexity is further reduced. Moreover, the proposed method is suitable for the case of spatially nonuniform colored

noise. Simulation results show the performance of the proposed method is comparable to those of the existing PM

method and the standa rd MUSIC method.

Keywords: Fast Algorithm, DOA Estimation, Subspace-Based Method

1. Introduction

DOA estimation of spatial signal source with an array of

sensors has been an active research problem in array sig-

nal processing due to its wide applications in radar, sonar

and so on. Many classical algorithms have been devel-

oped in the past thirties years [1-3], in particular, a class

of subspace-based methods such as MUSIC [1], Root-

MUSIC [2], and ESPRIT [3] are drawn more attractive

due to its higher resolution performance but without mul-

tiple-dimension search computation. However, most of

the subspace-based methods are required to compute the

eigendecomposition of covariance matrix of array output

data in order to obtain the so-called signal subspace or

noise subspace, which its application is limited in case of

larger number of array sensors. To avoid the computa-

tional load of the eigendecomposition of covariance ma-

trix, in recent years, some fast algorithms for DOA esti-

mation have been proposed for certain condition in the

literature [4-7]. In particular, the propagation method (PM)

[6,7] without eigendecomposition has been discussed due

to lower computational load. However, the available PM

method need use the whole covariance of array output

data to obtain the propagation operator, therefore, the

PM-based algorithm is only suitable to the presence of

white Gaussian noise, and its performance will be de-

graded in spatial nonuniform colored noise [8].

In this paper, we present a modified PM algorithm for

DOA estimation with an ULA, a different computation

method for the propagation operator is given, which is

only obtained by the partially cross-correlation of array

output data. As a result, the proposed algorithm is com-

putationally simpler than the available PM method [6].

Moreover, the proposed algorithm is suitable for the case

of spatially nonuniform colored noise due to using the

off-diagonal elements of array covariance matrix.

2. Proposed Method

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Let an uniform linear array of N sensors receive P

narrow band signals impinging from the sources with

unknown spatial DOA’s

1,,

. The sensor array

outputs can be expressed as:

,1,2,,tttt

xAsn L (1)